July

23rd July 2007



Use partial fractions to solve the integrals

16th July 2007



Use partial fractions to solve the integrals

9th July 2007
$f:y\mapsto y^2, \, y \in \Re$
$g:y\mapsto \sqrt{16-4y}, \, y\in \Re, \, y\leq 4$
$h:y\mapsto 5y+10, \, y\in \Re$
find
$f^{-1}, \, g^{-1} \,and \, h^{-1}$

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2th July 2007
given that
$f(x)=2x^2-14x+9, \, x \in \Re$
$g(x)=x^3+6, \, x>0, \, x \in \Re$
find
$f(-1), \, g(5), \, fg(2)$

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June

25th June 2007
Show that
$\dfrac{4x^3-7x+5}{2x+3}$
can be written as
$Ax^2+Bx+C+\frac{D}{2x+3}$
And calculate the values of A, B, C and D

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18th June 2007
Simplify the following

$\dfrac{2x^2-8}{4x^2+20x+24}$

$\dfrac{x^2-x-6}{x^3+6x^2+8x}$

$\dfrac{3(a+2)}{4b} \times \dfrac{b^2}{3(a^2-4)}$

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11th June 2007
Show that
$(x+1)$
is a factor of
$x^3-x^2-50x-48$

hence or otherwise find all the solutions of
$x^3-x^2-50x-48=0$

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4th June 2007
Solve the following

$\int\limits_{0}^{10} x^3+3x-\frac{1}{x^2}\, dx$

$\int \limits_{-5}^{5}2x^2-2x-\frac{1}{x}+\frac{1}{3x^3}\,dx$

$\int \limits_{1}^{3}\alpha^3-2\alpha^2-\frac{3}{\alpha}+\frac{2}{3\alpha^2}\,d\alpha$

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May

28th May 2007

The curve c has the equation f(x)= x³ - 7x² + 15x + 6
The point P has an x coordinate of 1
The point Q is a minimum turning point of the curve
Find f'(x) and show that PQ is parallel to the x-axis

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21th May 2007
$3\sin x=6\cos x$
find the value of
$\tan x$

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14th May 2007
solve for
$0^{\circ}<360^{\circ}$
$5 \sin^2 x=1+ \cos x$
Giving your answer to the nearest degree

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7th May 2007
Describe the circle with the equation
$x^2+y^2=4x$

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April

30th April 2007
A cylinder of radius x and height y has a surface area of 60cm². Calculate the maximum volume of the cylinder.

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23rd April 2007
Expand (4 + ax)⁶ in ascending powers of x up to the term in x³
if the coefficient of x³ is 20. what is the value of a
Now substitute for a to work out the coefficients of the other three parts

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16th April 2007
Factorise
$x^3- 7x - 6$

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2nd April 2007
A circle C has centre
$(4,3)$
and radius
$5\sqrt{2}$
A line L has the equation y=x+3
a) Write down the equation of circle C
b) Calculate the exact coordinates of the two points where C intersects L
c) Find the distance between the two points

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March

26th March 2007

The line
$y=x+5$
cuts the line
$y=x^2+6x-12$
at the points A and B
(a) Find the coordinates of A and B
(b) Calculate the area between the two lines

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19th March 2007
If log3(x) = log5(y), find in the form of a single logarithm, the value of logx(y).

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12th March 2007
The coefficient of x² in the binomial expansion of
$(1+\frac{x}{2})^n$
where n is a positive integer, is 9.
(changed coefficient to 9 to make life easier - but how to answer it is still your problem)
a) find the value of n.
b) Using the value of n found in part a, find the coefficient of x³.

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5th March 2007

Work out (a) The area and (b) The perimeter of the blue shape.

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February

26th Feb 2007
a) work out the other angles here:

b) now work out its area.

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19th Feb 2007
if
$a+b+c=4$
$ab+bc+ca=6$
$abc=3$
Work out
$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}$
$\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}$
$a^2+b^2+c^2$